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 A116217 Decimal expansion of constant Sum_{i,j,k=1..inf} 1/2^(i*j*k). 0
 2, 3, 2, 4, 7, 8, 4, 7, 7, 2, 8, 4, 0, 4, 7, 9, 0, 6, 1, 2, 3, 5, 2, 1, 7, 6, 8, 2, 8, 6, 1, 3, 9, 3, 0, 4, 6, 0, 2, 0, 9, 5, 1, 3, 4, 5, 2, 2, 5, 4, 7, 6, 0, 5, 3, 6, 0, 1, 4, 6, 9, 4, 6, 4, 4, 4, 1, 9, 2, 2, 0, 2, 0, 0, 4, 6, 3, 9, 7, 7, 0, 3, 1, 7, 3, 6, 9, 8, 8, 4, 0, 1, 5, 1, 2, 7, 7, 2, 8, 2, 6, 8, 8, 3, 1 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This constant is a sum of triple series Sum[Sum[Sum[1/2^(i*j*k),{i,1,Infinity}],{j,1,Infinity}],{k,1,Infinity}] = 2.3247847... It is similar to Erdos-Borwein constant Sum[Sum[1/2^(i*j),{i,1,Infinity}],{j,1,Infinity}] = Sum[1/(2^k-1),{k,1,Infinity}] = 1.60669515... LINKS Eric Weisstein's World of Mathematics, Triple Series. FORMULA Equals Sum_{n=1..infinity} A007425(n)/2^n . - R. J. Mathar, Jan 23 2008 From Amiram Eldar, Aug 10 2020: (Start) Equals Sum{k>=1} d(k)/(2^k - 1), where d(k) is the number of divisors of k (A000005). Equals Sum_{i,j=1..oo} 1/(2^(i*j) - 1). (End) EXAMPLE 2.32478477284047906123521768286139304602095134522547605... MATHEMATICA digits = 105; Clear[s]; s[n_] := s[n] = 2*NSum[1/(2^(j*k) - 1), {j, 1, n}, {k, 1, j-1}, WorkingPrecision -> digits+10, NSumTerms -> 100] + NSum[1/(2^j^2 - 1), {j, 1, n}, WorkingPrecision -> digits+10, NSumTerms -> 100] // RealDigits[#, 10, digits]& // First; s[n=100]; While[s[n] != s[n-100], n = n+100]; s[n] (* Jean-François Alcover, Feb 13 2013 *) PROG (PARI): /* Using sum(n=1..infinity, A007425(n)/2^n )  */ lambert2ser(L)= {     local(n, t);     n = length(L);     t = sum(k=1, length(L), O('x^(n+1))+L[k]*'x^k/(1-'x^k) );     t = Vec(t);     return( t ); } N=1000; v=vector(N, n, 1); /* roughly 1000 bits precision */ t=lambert2ser(lambert2ser(v)); /* ==[1, 3, 3, 6, 3, 9, ...] == A007425 */ default(realprecision, floor(N/3.4)); /* factor approx. log(10)/log(2) */ sum(n=1, #v, 1.0*t[n]/2^n) /* == 2.324784772840479061235217682861... */ CROSSREFS Cf. A065442 = Decimal expansion of Erdos-Borwein constant Sum_{k=1..inf} 1/(2^k-1). Cf. A000005, A007425. Sequence in context: A303845 A132439 A338902 * A333907 A274486 A227961 Adjacent sequences:  A116214 A116215 A116216 * A116218 A116219 A116220 KEYWORD cons,nonn AUTHOR Alexander Adamchuk, Apr 09 2007 EXTENSIONS More terms from R. J. Mathar, Jan 23 2008 More terms from Jean-François Alcover, Feb 13 2013 STATUS approved

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Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)